2025/09/20 by Shota Maehara, Maehara, Shota · 1 citation
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #advanced mathematical theories #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2509.16569
openalex publication_date 2025/09/20 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28
In the theory of hyperplane arrangements, M. Wakefield and S. Yuzvinsky utilized a square matrix in their research on the exponents of 2-dimensional multiarrangements. Using such a matrix, they showed that the exponents of 2-dimensional multiarrangements are as close as possible in general position for any fixed balanced multiplicity. In this article, we introduce a matrix similar to that of Wakefield and Yuzvinsky and explore further applications to the exponents. In fact, the exponents of 2-dimensional multiarrangements are determined by whether the corresponding matrices have full rank. As one of our main results, we introduce a new class of 2-dimensional arrangements for which the exponents are as close as possible for any balanced multiplicities, except for the constant one multiplicity. We also proceed with the classification of B2-exponents, and we provide an alternative proof for some known results on the exponents.